Is the word lava the same in Brazilian and European Portuguese?

Yes

The spelling, meaning, and grammatical function of the word "lava" (both as the molten rock and as the third-person singular of the verb lavar) are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the unstressed final "a" is generally more open and clearly articulated. In Continental Portuguese, unstressed final vowels undergo significant reduction, meaning the "a" sounds much more closed, neutralized, or even almost swallowed.

Brazilian Portuguese Examples

1. A lava está saindo do vulcão. (The lava is coming out of the volcano.)
2. A lava é muito quente. (The lava is very hot.)
3. Ele lava o carro todo final de semana. (He washes the car every weekend.)
4. A lava escorreu pela montanha. (The lava flowed down the mountain.)
5. A lava esfriou e virou pedra. (The lava cooled and turned into stone.)

Continental Portuguese Examples

1. A lava está a sair do vulcão. (The lava is coming out of the volcano.)
2. A lava é extremamente quente. (The lava is extremely hot.)
3. Ele lava o carro todos os fins de semana. (He washes the car every weekend.)
4. A lava escorreu pela montanha. (The lava flowed down the mountain.)
5. A lava arrefeceu e tornou-se pedra. (The lava cooled and became stone.)